If the function `f(x)=sin^(-1)x+cos^(-1)x` and g(x) are identical, then g(x) can be equal to

Options

A. `sin^(-1)|x|+|cos^(-1)x|`
B. `tan^(-1)x+cot^(-1)x`
C. `|sin^(-1)x|+cos^(-1)|x|`
D. `(sqrt(sin^(-1)x))^(2)+(sqrt(cos^(-1)x))^(2)`

Answer

C

Explanation

`f(x)=sin^(-1)x + cos^(-1)x=(pi)/(2), AA x in [-1,1]`
If `g(x)=|sin^(-1)x|+cos^(-1)|x|={{:(-sin^(-1)x +pi-cos^(-1)x, -1le x lt 0),(=pi-(pi)/(2)=(pi)/(2)),(sin^(-1)x + cos^(-1)x, 0le x le 1),(=(pi)/(2)):}`